"Better" is very subjective. A perfect system (immediately doing everything medically possible) doesn't exist.
In the USA, the system is "better" in that it provides excellent service without significant delay, but to achieve this it restricts access by being significantly expensive to the patient (or their employer).
That means that far too many people simply don't get even basic medical service.
In Canada (varies by province) service is good and effectively free, but this is achieved by having significantly longer wait times for non-emergencies.
Questions and Answers - Ontario Health Insurance Plan lists eligibility for Ontario's OHIP card:
- you make your primary place of residence in Ontario;
- you are in Ontario for at least 153 days of the first 183 days immediately following the date you establish residence in Ontario (you cannot be absent for more than 30 days during the first 6 months of residence);
- you are in Ontario for at least 153 days in any 12-month period.
Which means you won't be eligible for the first 6 months.
Read that linked section and what follows for more details, and how to apply for a card.
Visitors and new immigrants can purchase private medical insurance until eligible for OHIP.
Ontario health insurance for Newcomers | Moving2Canada provides more information.
Assuming it is up-to-date, it also says:
However, during COVID-19, Ontario has waived the traditional three-month waiting period for OHIP coverage for newcomers and recent immigrants.
They do plan to reinstate it in the future.
This means that if you entered Canada after March 19th, 2020, and settled in Ontario, you should have immediate access to OHIP.
Whatever the case, you should visit in person an Ontario Service Centre to apply as soon as you can.
Be sure to bring your appropriate identification and immigration documents.